The antonyms for the phrase "more noncompulsory" are "mandatory" or "obligatory." These words convey a sense of something that is required or necessary, rather than optional or discretionary. When something is mandatory, there is no choice but to do it, whereas noncompulsory implies the option to opt out or decline. Obligatory, on the other hand, implies a certain moral or ethical duty to do something, while noncompulsory suggests that there is no moral imperative to act. Thus, the opposite of "more noncompulsory" is something that is binding or necessary, rather than discretionary or voluntary.